Question

The sum and difference of two vector are equal in magnitude. Find the angle between two vectors

Answer 1

Logically, how can magnitude of vector sum be equal to difference of their magnitudes. Obviously if the vectors are in opposite directions. This means the angle has to be 180.

Mathematically,

Let the vectors be a and b with magnitudes a and b respectively and the angle between them be x.

Magnitude of the sum of a and b is

√(a^2+b^2+2abcosx

Difference in their magnitudes is

a-b

Hence,

√(a^2+ b^2+2ab cosx) = a-b

Squaring both sides,

a^2+b^2+2ab cos x = a^2+ b^2–2ab

2ab cosx+2ab =0

2ab(cosx +1) =0

Since 2ab can't be zero,

Cos x+1=0

Cosx=-1

X=180

if you are satisfy with my ans then mark me as a brainlist

if there is something wrong then kindly rectify it

Answer 2

Answer:

At 90 the sum of the two vector is 0